condition of existence of limit evaluation of right hand left hand limit

Right Hand Rule

Right Hand Rule

Examples of right handed helix is/are

A number consists of three digits which are in GP the sum of the right hand digits exceeds twice the middle digits by 1 and the sum of the left hand and middle digits is two thirs of the sum of the middle and right hand digits. Find the number.

If f(x)=(1)/(1+e^(-(1)/(x))),x!=0 and 0,x=0 then at x=0 (A) right hand limit of f(x) exists but not left-hand limit (B) limit of f(x) exists but not but not right-hand limit (C) both limits exists but are not equal (D) both limits exist and are equal